Convex Combinations of Minimal Graphs. (15th August 2012) - Dorff, Michael; Viertel, Ryan; Wołoszkiewicz, Magdalena
Abstract : Given a collection of minimal graphs, M 1, M 2, …, M n, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions on M 1, M 2, …, M n so that a convex combination of them will be a minimal graph. We will then provide two examples, taking a convex combination of Scherk's doubly periodic surface with the catenoid and Enneper's surface, respectively.